# What is a Line Segment

By the end of this lesson, you will be able to

- define line segment in geometry.
- describe types of line segment.
- demonstrate examples of line segment.
- distinguish between line segment and line.
- compare open line segment and closed line segment.
- interpret half-open line segment.

## Line Segment

A line segment, having two distinct end points, is a definite part of a line containing all the points between the endpoints.

Let's go to discuss the line segment definition geometry explicitly.

A line is shown in the figure above that doesn't have any endpoints.

Let A and B be the two distinct points on the line.

Cut the portion AB and isolate that is shown in the following figure.

That is the line segment AB.

A and B are two endpoints of line segment AB. And it also contains all the points between A and B.

### Line Segment Example

## Types of Line Segment

Generally, line segment is divided into the following parts:

- Closed line segment
- Open line segment
- Half-Open line segment

### Closed line segment

A line segment is said to be a closed line segment if it contains both endpoints.

A line segment AB is shown in the figure.

A and B are two endpoints. The line segment AB contains all the points on AB including A and B.

Thus AB is a closed line segment.

It is denoted by [A,B]

### Open line segment

A line segment is said to be open if it contains all the point on the line segment except both endpoints.

A line line segment AB is shown in the figure.

A and B are two endpoints. The line segment AB contains all the points on AB excluding both A and B.

Thus AB is a open line segment.

It is denoted by (A,B)

### Half-Open line segment

A line segment is said to be half-open if it contains only one of the endpoints.

Line segment definition geometry includes two types of half-open line segment.

A line segment is shown in the followong figure.

This line segment contains all the points including end point B and excluding endpoint A.

That is; it contains only one of the endpoints.

Hence, it is a half-open line segment.

It is denoted by (A,B].

Again, a line segment is shown in the followong figure.

This line segment contains all the points including end point A and excluding endpoint B.

That is; it contains only one of the endpoints.

Hence, it is also a half-open line segment.

And it is denoted by [A,B).